| /* |
| Copyright (c) 2004-2006, The Dojo Foundation |
| All Rights Reserved. |
| |
| Licensed under the Academic Free License version 2.1 or above OR the |
| modified BSD license. For more information on Dojo licensing, see: |
| |
| http://dojotoolkit.org/community/licensing.shtml |
| */ |
| |
| dojo.provide("dojo.math"); |
| |
| dojo.math.degToRad = function(/* float */x) { |
| // summary |
| // Converts degrees to radians. |
| return (x*Math.PI) / 180; // float |
| } |
| dojo.math.radToDeg = function(/* float */x) { |
| // summary |
| // Converts radians to degrees. |
| return (x*180) / Math.PI; // float |
| } |
| |
| dojo.math.factorial = function(/* integer */n){ |
| // summary |
| // Returns n! |
| if(n<1){ return 0; } |
| var retVal = 1; |
| for(var i=1;i<=n;i++){ retVal *= i; } |
| return retVal; // integer |
| } |
| |
| dojo.math.permutations = function(/* integer */n, /* integer */k) { |
| // summary |
| // The number of ways of obtaining an ordered subset of k elements from a set of n elements |
| if(n==0 || k==0) return 1; |
| return (dojo.math.factorial(n) / dojo.math.factorial(n-k)); // float |
| } |
| |
| dojo.math.combinations = function (/* integer */n, /* integer */r) { |
| // summary |
| // The number of ways of picking n unordered outcomes from r possibilities |
| if(n==0 || r==0) return 1; |
| return (dojo.math.factorial(n) / (dojo.math.factorial(n-r) * dojo.math.factorial(r))); // float |
| } |
| |
| dojo.math.bernstein = function(/* float */t, /* float */n, /* float */i) { |
| // summary |
| // Calculates a weighted average based on the Bernstein theorem. |
| return (dojo.math.combinations(n,i) * Math.pow(t,i) * Math.pow(1-t,n-i)); // float |
| } |
| |
| dojo.math.gaussianRandom = function(){ |
| // summary |
| // Returns random numbers with a Gaussian distribution, with the mean set at 0 and the variance set at 1. |
| var k = 2; |
| do { |
| var i = 2 * Math.random() - 1; |
| var j = 2 * Math.random() - 1; |
| k = i * i + j * j; |
| } while (k >= 1); |
| k = Math.sqrt((-2 * Math.log(k)) / k); |
| return i * k; // float |
| } |
| |
| dojo.math.mean = function() { |
| // summary |
| // Calculates the mean of an Array of numbers. |
| var array = dojo.lang.isArray(arguments[0]) ? arguments[0] : arguments; |
| var mean = 0; |
| for (var i = 0; i < array.length; i++) { mean += array[i]; } |
| return mean / array.length; // float |
| } |
| |
| dojo.math.round = function(/* float */number, /* integer */places) { |
| // summary |
| // Extends Math.round by adding a second argument specifying the number of decimal places to round to. |
| // TODO: add support for significant figures |
| if (!places) { var shift = 1; } |
| else { var shift = Math.pow(10, places); } |
| return Math.round(number * shift) / shift; // float |
| } |
| |
| dojo.math.sd = dojo.math.standardDeviation = function(/* array */){ |
| // summary |
| // Calculates the standard deviation of an Array of numbers |
| var array = dojo.lang.isArray(arguments[0]) ? arguments[0] : arguments; |
| return Math.sqrt(dojo.math.variance(array)); // float |
| } |
| |
| dojo.math.variance = function(/* array */) { |
| // summary |
| // Calculates the variance of an Array of numbers |
| var array = dojo.lang.isArray(arguments[0]) ? arguments[0] : arguments; |
| var mean = 0, squares = 0; |
| for (var i = 0; i < array.length; i++) { |
| mean += array[i]; |
| squares += Math.pow(array[i], 2); |
| } |
| return (squares / array.length) - Math.pow(mean / array.length, 2); // float |
| } |
| |
| dojo.math.range = function(/* integer */a, /* integer */b, /* integer */step) { |
| // summary |
| // implementation of Python's range() |
| if(arguments.length < 2) { |
| b = a; |
| a = 0; |
| } |
| if(arguments.length < 3) { |
| step = 1; |
| } |
| |
| var range = []; |
| if(step > 0) { |
| for(var i = a; i < b; i += step) { |
| range.push(i); |
| } |
| } else if(step < 0) { |
| for(var i = a; i > b; i += step) { |
| range.push(i); |
| } |
| } else { |
| throw new Error("dojo.math.range: step must be non-zero"); |
| } |
| return range; // array |
| } |